From Risk & Return Models to Hurdle Rates:
Estimation Challenges
Inputs required to use the CAPM  Expected Return = Riskfree Rate+ Beta *
(Expected Return on the Market
Portfolio - Riskfree Rate)
To use the model we need three inputs:
a. The current risk-free rate
b. The expected market risk premium (the
premium expected for investing in risky
assets (market portfolio) over the
riskless asset)
c. The beta of the asset being analyzed.
Riskfree Rates
The Riskfree Rate
• For an investment to be riskfree two
conditions have to be met –
– There has to be no default risk, which
generally implies that the bond has to
be issued by the government.
– There can be no uncertainty about
reinvestment rates, which implies that it
is a zero coupon bond with the same
maturity as the cash flow being analyzed.
Vocabulary
• Default Risk – The chances that the
issuer of the bond will not repay the
bond in full when it matures.
Riskfree Rates
• Using a government bond rate (even on a
coupon bond) as the riskfree rate on all of
the cash flows in a long term analysis will
give a very close estimate of the true value.
• The riskfree rate that you use in an
analysis should be in the same currency
that your cashflows are estimated in.
– If your cash flows are in Euros, your
riskfree rate should be a Euro riskfree
rate.
Check 10 year bond rates
• http://www.bloomberg.com/markets/ratesbonds/
What is the Euro riskfree rate? An exercise in
2009
The Euro rates: A 2012 update
What about risky government bonds?
• If the government is perceived to have default
risk, the government bond rate will have a
default spread component in it and not be
riskfree. There are three choices we have, when
this is the case.
– Adjust the local currency government
borrowing rate for default risk to get a riskless
local currency rate.
• In May 2009, the Indian government rupee
bond rate was 7%. the local currency rating
from Moody’s was Ba2 and the default
spread for a Ba2 rated country bond was
3%.
Riskfree rate in Rupees = 7% - 3% = 4%
• In May 2009, the Brazilian government $R
bond rate was 11% and the local currency
rating was Ba1, with a default spread of
2.5%.
Riskfree rate in $R = 11% - 2.5% = 8.5%
What about risky government
bonds?
– Do the analysis in an alternate currency,
where getting the riskfree rate is easier.
With Aracruz in 2009, we could chose to
do the analysis in US dollars (rather than
estimate a riskfree rate in R$). The
riskfree rate is then the US treasury
bond rate.
– Do your analysis in real terms, in which
case the riskfree rate has to be a real
riskfree rate. The inflation-indexed
treasury rate is a measure of a real
riskfree rate.
• http://www.bloomberg.com/news/2013-0321/treasury-sells-tips-at-negative-yields-asbuyers-doubt-bernanke.html
• http://ycharts.com/indicators/10_year_treas
ury_inflation_indexed_security_rate
Questions
• How should we calculate the riskfree
rate if we are expecting cashflows for 5
years in Euros?
• How should we calculate the riskfree
rate if we are expecting cashflows in
Chinese RMB?
Equity Risk Premiums
Measurement of the risk premium
• The risk premium is the premium that
investors demand for investing in an
average risk investment, relative to the
riskfree rate.
• As a general proposition, this premium
should be
– greater than zero
– increase with the risk aversion of the
investors in that market
– increase with the riskiness of the
What is your risk premium?
 Assume that stocks are the only risky assets and that you are
offered two investment options:
 a riskless investment (say a Government Security), on which
you can make 5%
 a mutual fund of all stocks, on which the returns are
uncertain
 How much of an expected return would you demand to shift
your money from the riskless asset to the mutual fund?
a. Less than 5%
b. Between 5 - 7%
c. Between 7 - 9%
d. Between 9 - 11%
e. Between 11- 13%
f. More than 13%
Risk Aversion and Risk Premiums
• If this were the entire market, the risk
premium would be a weighted average of the
risk premiums demanded by each and every
investor.
• The weights will be determined by the wealth
that each investor brings to the market. Thus,
Warren Buffett’s risk aversion counts more
towards determining the “equilibrium”
premium than yours’ and mine.
• As investors become more risk averse, you
would expect the “equilibrium” premium to
increase.
Risk Premiums do change..
• Go back to the previous example. Assume
now that you are making the same choice
but that you are making it in the aftermath
of a stock market crash (it has dropped
25% in the last month). Would you change
your answer?
a. I would demand a larger premium
b. I would demand a smaller premium
c. I would demand the same premium
Estimating Risk Premiums in Practice
• Survey investors on their desired risk
premiums and use the average premium
from these surveys.
• Assume that the actual premium delivered
over long time periods is equal to the
expected premium - i.e., use historical data
• Estimate the implied premium in today’s
asset prices.
The Survey Approach
• Surveying all investors in a market place is
impractical.
• However, you can survey a few individuals
and use these results. In practice, this
translates into surveys of the following:
• The limitations of this approach are:
– There are no constraints on reasonability
– The survey results are more reflective of
the past than the future.
– They tend to be short term; even the
longest surveys do not go beyond one
year.
Survey
The Historical Premium Approach
• This is the default approach used by most to
arrive at the premium to use in the model
• In most cases, this approach does the
following
– Defines a time period for the estimation
(1928-Present, 1962-Present....)
– Calculates average returns on a stock index
during the period
– Calculates average returns on a riskless
security over the period
– Calculates the difference between the two
averages and uses it as a premium looking
forward.
The Historical Premium Approach
• The limitations of this approach are:
– it assumes that the risk aversion of
investors has not changed in a
systematic way across time. (The risk
aversion may change from year to year,
but it reverts back to historical averages)
– it assumes that the riskiness of the
“risky” portfolio (stock index) has not
changed in a systematic way across time.
B. The Historical Risk Premium
Evidence from the United States
1928-2012
1962-2012
2002-2012
Arithmetic Average
Geometric Average
Stocks - T. Bills Stocks - T. Bonds Stocks - T. Bills Stocks - T. Bonds
7.65%
5.88%
5.74%
4.20%
2.20%
2.33%
5.93%
3.91%
4.60%
2.93%
2.38%
2.66%
7.06%
3.08%
5.38%
1.71%
5.82%
8.11%
What is the right premium?
• Go back as far as you can. Otherwise, the standard error in
the estimate will be large.
Annualized Std deviation in Stock prices
)
Number of years of historical data
riskfree rate.
Std Error in estimate =
• Be consistent in your use of a
• Use arithmetic premiums for one-year estimates of costs of
equity and geometric premiums for estimates of long term
costs of equity.
What about historical premiums for other
markets?
• Historical data for markets outside the
United States is available for much shorter
time periods. The problem is even greater
in emerging markets.
• The historical premiums that emerge from
this data reflects this data problem and
there is much greater error associated with
the estimates of the premiums.
One solution: Look at a country’s bond rating
and default spreads as a start
• Ratings agencies assign ratings to countries
that reflect their assessment of the default
risk of these countries. These ratings reflect
the political and economic stability of these
countries and thus provide a useful measure
of country risk.
– India has a rating of Ba2 from Moody’s.The
typical default spread for Ba2 rated
sovereign bonds is 3%.
• Many analysts add this default spread to the
US risk premium to come up with a risk
premium of 6.88% for India, if we use 3.88%
as the premium for the US (3.88% was the
historical risk premium for the US from 19282008)
Beyond the default spread
• While default risk spreads and equity risk
premiums are highly correlated, one would
expect equity spreads to be higher than debt
spreads.
• Risk Premium for Brazil in 2009
– Standard Deviation in Bovespa (Equity) = 34%
– Standard Deviation in Brazil $ denominated
Bond = 21.5%
– Default spread on $ denominated Bond =
2.5%
– Country Risk Premium (CRP) for Brazil = 2.5%
(34%/21.5%) = 3.95%
– Total Risk Premium for Brazil = US risk
premium (in ‘09) + CRP for Brazil
= 3.88% + 3.95% = 7.83%
Question- Calculate the Risk
Premium
• Risk Premium for India in May 2009
– Standard Deviation in Sensex (Equity) =
32%
– Standard Deviation in Indian
government bond = 21.3%
– Default spread based upon rating= 3%
– Country Risk Premium for India =
Default Spread * (SDE/SDB) = ?
– Total Risk Premium for India = US risk
premium in 09 (3.88%) + CRP for India
=?
An alternate view of ERP: Looking
forward
Between 2001 and 2007
dividends and stock
buybacks averaged 4.02%
of the index each year.
Analysts expect earnings to grow 5% a year for the next 5 years. We
will assume that dividends & buybacks will keep pace..
Last year’s cashflow (59.03) growing at 5% a year
61.98
January 1, 2008
S&P 500 is at 1468.36
4.02% of 1468.36 = 59.03
65.08
68.33
71.75
After year 5, we will assume that
earnings on the index will grow at
4.02%, the same rate as the entire
economy (= riskfree rate).
75.34
Solving for the implied premium…
• If we know what investors paid for equities at
the beginning of 2007 and we can estimate
the expected cash flows from equities, we can
solve for the rate of return that they expect to
make (IRR):
1468.36 =
61.98 65.08
68.33
71.75
75.34
75.35(1.0402)
+
+
+
+
+
(1+ r) (1+ r) 2 (1+ r) 3 (1+ r) 4 (1+ r) 5 (r - .0402)(1+ r) 5
• Expected Return on Stocks = 8.39%
• Implied Equity Risk Premium = Expected
Return on Stocks - T.Bond Rate =8.39% 4.02% = 4.37%
A year that made a difference.. The implied
premium in January 2009
Year
2001
2002
2003
2004
2005
2006
2007
2008
Normalized
Market value of index
1148.09
879.82
1111.91
1211.92
1248.29
1418.30
1468.36
903.25
903.25
Dividends
15.74
15.96
17.88
19.01
22.34
25.04
28.14
28.47
28.47
Buybacks
14.34
13.87
13.70
21.59
38.82
48.12
67.22
40.25
24.11
Cash to equity Dividend yield Buyback yield
30.08
1.37%
1.25%
29.83
1.81%
1.58%
31.58
1.61%
1.23%
40.60
1.57%
1.78%
61.17
1.79%
3.11%
73.16
1.77%
3.39%
95.36
1.92%
4.58%
68.72
3.15%
4.61%
52.584
3.15%
2.67%
Total yield
2.62%
3.39%
2.84%
3.35%
4.90%
5.16%
6.49%
7.77%
5.82%
Implied ERP from September 12, 2008 to
January 1, 2009
Equity Risk Premiums in early 2009
• Mature Markets: In May 2009, the number
that we chose to use as the equity risk
premium for all mature markets was 6%.
While lower than the implied premium at the
start of the year 6.43%, it is still much higher
than the historical risk premium of 3.88%. It
reflected our beliefs then that while the crisis
was abating, it would leave a longer term
impact on risk premiums.
Equity Risk Premiums in early
2009
• For emerging markets, we will use the melded
default spread approach (where default
spreads are scaled up to reflect additional
equity risk) to come up with the additional
risk premium.
– ERP for Brazil = Mature market premium +
CRP for Brazil = 6% + 3.95% = 9.95%
– ERP for India = Mature market premium +
CRP for India = 6% + 4.51% = 10.51%
An Updated Equity Risk Premium:
• On January 1, 2013, the S&P 500 was at
1426.19, essentially unchanged for the
year. And it was a year of macro shocks
– political upheaval in the Middle East
and sovereign debt problems in Europe.
The treasury bond rate dropped below
2% and buybacks/dividends surged.
An Updated Equity Risk Premium:
Implied Premiums in the US: 1960-2012
A Composite way of estimating ERP for
countries
• Step 1: Estimate an equity risk premium for a
mature market. If your preference is for a forward
looking, updated number, you can estimate an
implied equity risk premium for the US. In
January 2013, an estimate for the implied
premium in the US was 5.8%. That will also be an
estimate for a mature market ERP.
• Step 2: Come up with a generic and measurable
definition of a mature market.
– An estimate: Any AAA rated country is mature.
A Composite way of estimating
ERP for countries
• Step 3: Estimate the additional risk
premium that you will charge for markets
that are not mature. You have two choices:
– The default spread for the country, estimated
based either on sovereign ratings or the CDS
market.
– A scaled up default spread, where you adjust
the default spread upwards for the additional
risk in equity markets.
Country
January
Belgium
Germany
Portugal
Italy
Risk Premiums
Luxembourg
Austria
2013
Denmark
France
Finland
Canada
USA
N. America
Argentina
Belize
Bolivia
Brazil
Chile
Colombia
Costa Rica
Ecuador
El Salvador
Guatemala
Honduras
Mexico
Nicaragua
Panama
Paraguay
Peru
Uruguay
Venezuela
Latin America
0.00% 5.80% Greece
0.00% 5.80% Iceland
0.00% 5.80% Ireland
Netherlands
Norway
Slovenia
9.00% 14.80%
Spain
15.00% 20.80%
Sweden
4.88% 10.68%
Switzerland
2.63% 8.43%
Turkey
1.05% 6.85%
UK
3.00% 8.80%
W.Europe
3.00% 8.80%
10.50% 16.30%
Angola
4.88% 10.68%
Botswana
3.60% 9.40%
Egypt
7.50% 13.30%
Kenya
2.25% 8.05%
Mauritius
9.00% 14.80%
Morocco
2.63% 8.43%
Namibia
6.00% 11.80%
Nigeria
2.63% 8.43%
Senegal
3.00% 8.80%
South Africa
6.00% 11.80%
Tunisia
3.38% 9.18%
Zambia
Africa
1.05%
0.00%
4.88%
2.63%
0.00%
0.00%
0.00%
0.38%
6.85%
5.80%
10.68%
8.43%
5.80%
5.80%
5.80%
6.18%
0.00%
5.80%
10.50%
3.00%
16.30%
8.80%
3.60%
9.40%
0.00%
0.00%
2.63%
3.00%
0.00%
0.00%
3.60%
0.00%
1.05%
5.80%
5.80%
8.43%
8.80%
5.80%
5.80%
9.40%
5.80%
6.85%
4.88%
1.50%
7.50%
6.00%
2.25%
3.60%
3.00%
4.88%
6.00%
2.25%
3.00%
6.00%
4.29%
10.68%
7.30%
13.30%
11.80%
8.05%
9.40%
8.80%
10.68%
11.80%
8.05%
8.80%
11.80%
10.09%
Albania
6.00%
Armenia
4.13%
Azerbaijan
3.00%
Belarus
9.00%
Bosnia & Herzego
vina
9.00%
Bulgaria
2.63%
Croatia
3.00%
Czech Republic
1.28%
Estonia
1.28%
Georgia
4.88%
Hungary
3.60%
Kazakhstan
2.63%
Latvia
3.00%
Lithuania
2.25%
Moldova
9.00%
Montenegro
4.88%
Poland
1.50%
Romania
3.00%
Russia
2.25%
Slovakia
1.50%
Ukraine
9.00%
E. Europe & Russ
ia
2.68%
Bahrain
Israel
Jordan
Kuwait
Lebanon
Oman
Qatar
Saudi Arabia
United Arab Emirates
Middle East
11.80%
9.93% Bangladesh
8.80% Cambodia
China
14.80%
4.88%
7.50%
1.05%
Fiji Islands
6.00%
Hong Kong
0.38%
14.80% India
3.00%
8.43% Indonesia
3.00%
8.80% Japan
1.05%
7.08% Korea
1.05%
7.08% Macao
1.05%
1.73%
10.68% Malaysia
Mongolia
6.00%
9.40%
10.50%
8.43% Pakistan
Papua
New
Guinea
6.00%
8.80%
3.60%
8.05% Philippines
Singapore
0.00%
14.80%
Sri Lanka
6.00%
10.68% Taiwan
1.05%
7.30% Thailand
2.25%
8.80% Vietnam
7.50%
8.05% Asia
1.55%
10.68%
13.30%
6.85%
11.80%
6.18%
8.80%
8.80%
6.85%
6.85%
6.85%
7.53%
11.80%
16.30%
11.80%
9.40%
5.80%
11.80%
6.85%
8.05%
13.30%
7.35%
7.30%
14.80%
8.48%
2.25% 8.05%
1.28% 7.08%
4.13% 9.93%
0.75% 6.55%
6.00% 11.80%
1.28% 7.08%
0.75% 6.55%
1.05% 6.85%
0.75% 6.55%
1.16% 6.96%
Australia
0.00% 5.80%
New Zealand 0.00% 5.80%
Australia &
NZ
0.00% 5.80%
Black #: Total ERP
Red #: Country risk premium
AVG: GDP weighted averag
Estimating ERP for a Company: countries of
operation
• Incorporation: The conventional practice on
equity risk premiums is to estimate an ERP
based upon where a company is
incorporated.
• Operation: The more sensible practice on
equity risk premium is to estimate an ERP
based upon where a company operates. For
a company like Coca Cola, for instance, using
its revenue breakdown in 2011
geographically, this would lead to:
Estimating ERP for a Company:
countries of operation
Questions
• What does equity risk premium mean?
• Do you prefer the implied or historical
approcah to estimating equity risk
premiums?
• How do we estimate the equity risk
premium for global companies, e.g
McDonalds?
Homework: Estimating a Market Risk Premium
• For your company, get the geographical
breakdown of revenues in the most recent
year. Based upon this revenue breakdown
and the most recent country risk premiums,
estimate the equity risk premium that you
would use for your company.
• This computation was based entirely on
revenues. With your company, what
concerns would you have about your
estimate being too high or too low?